Hello, sri340!
Another approach (very primitive) . . .
In a 1000-m race, $\displaystyle A$ beats $\displaystyle B$ by 200 meters and $\displaystyle A$ beats $\displaystyle C$ by 500 meters.
Assuming that the contestants run at constant speeds, by how many meters does $\displaystyle B$ beat $\displaystyle C$?
. . $\displaystyle (A)\;300 \qquad(B)\;375 \qquad (C)\;450 \qquad (D)\;500 \qquad (E)\; 625$
The race ended like this: Code:
C B A
+ - - - - - - - - - o - - - - - o - - - o
0 500 800 1000
$\displaystyle C$ ran 500 m in the time that $\displaystyle B$ ran 800 m.
C's speed is $\displaystyle \tfrac{500}{800} = \tfrac{5}{8}$ of $\displaystyle B$'s speed.
When $\displaystyle B$ ran his last 200 m, $\displaystyle C$ ran only: .$\displaystyle \tfrac{5}{8}(200) \,=\,125$ m.
As $\displaystyle B$ crosses the finish line, $\displaystyle C$ is at the 625-m mark.
Therefore, $\displaystyle B$ beats $\displaystyle C$ be 375 m . . . answer (B).